Brine solution is the concentrated solution of NaCl in water.
NaCl(aq.)→Na(aq) ++Cl(aq) +
The cathode will attract the sodium ions from the sodium chloride and hydrogen ions from the water. The hydrogen ions gain 2 electrons and are reduced to form hydrogen molecules.
2H+(aq)+2e−→H2(g)
2H2O+2e−→H2(g)+2OH−(aq)
The anode will attract the hydroxide ions from the water and chlorine ions from sodium chloride. The chlorine ions lose 2 electrons and get oxidised.
Cl2→2Cl−+2e−
Na++OH−→NaOH